
Minimax Theory and its Applications 01 (2016), No. 1, 051063 Copyright Heldermann Verlag 2016 Representation of Viscosity Solutions of HamiltonJacobi Equations Emmanuel N. Barron Department of Mathematics and Statistics, Loyola University, Chicago, IL 60660, U.S.A. ebarron@luc.edu [Abstractpdf] Hamilton Jacobi equations of the form $H(x,u,Du)=0$ are considered with $H(x,r,p)$ nondecreasing in $r$ and quasiconvex in $p$. A viscosity solution may be represented as the value function of a calculus of variations or control problem in $L^\infty$, i.e., as a minimax problem. For time dependent problems of the form $u_t+H(t,x,u,Du)=0$ we require that $H(t,x,r,p)$ is convex in $p$ and nondecreasing in $r$. The viscosity solution is then given as the value of an $L^\infty$ problem. Keywords: Quasiconvex, HamiltonJacobi, representation. MSC: 35F21, 49L25 [ Fulltextpdf (148 KB)] for subscribers only. 